groebner_basis for multivariate polynomial ring with no variables

[dkrenn]

On all of the following examples, the warning

Warning: falling back to very slow toy implementation.

appear:

            sage: P = PolynomialRing(QQ, 't', 0)
            sage: P.ideal([P(2)]).groebner_basis()
            [1]
            sage: P.ideal([]).groebner_basis()
            []
            sage: P.ideal([0]).groebner_basis()
            []
            sage: P.ideal([3,4,0,5]).groebner_basis()
            [1]

Handle these cases separately! (Reason: singular does not handle these cases.)

[dkrenn]

New commits:

​9d4ffa6

Trac #27445: groebner basis for multi-variate polynomial ring with no variables

[embray]

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

[tscrim]

Can you also add a test when the base ring is not a field (e.g., ZZ)? Otherwise LGTM.

[dkrenn]

Replying to tscrim:

Can you also add a test when the base ring is not a field (e.g., ZZ)? Otherwise LGTM.

A test would always result in

TypeError: Can only reduce polynomials over fields.

also with this patch. Is this what you mean? (The situation for non-fields is more complex as coefficients do not need to divide each other...)

[tscrim]

Replying to dkrenn:

Replying to tscrim:

Can you also add a test when the base ring is not a field (e.g., ZZ)? Otherwise LGTM.

A test would always result in

TypeError: Can only reduce polynomials over fields.

also with this patch. Is this what you mean? (The situation for non-fields is more complex as coefficients do not need to divide each other...)

I believe that in general, but over ZZ Singular does GB computations:

sage: R.<x,y,z> = ZZ[]
sage: R.ideal([x^2-y,x*y-z*y+2,5*x*z-x]).groebner_basis()
[y*z^2 - y^2 - 2*x - 2*z, x^2 - y, x*y - y*z + 2, 5*y^2 - y*z + 10*x + 2, 5*x*z - x, 5*y*z - y, 10*z - 2]
sage: R.ideal([5,2]).groebner_basis()
[1]

So since singular works for ZZ, I think this patch should also fix it at least for that ring.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​6afce66

Trac #27445: polynomial rings over non-fields + major restructure of relevant code

[dkrenn]

Replying to tscrim:

I believe that in general, but over ZZ Singular does GB computations:

sage: R.<x,y,z> = ZZ[]
sage: R.ideal([x^2-y,x*y-z*y+2,5*x*z-x]).groebner_basis()
[y*z^2 - y^2 - 2*x - 2*z, x^2 - y, x*y - y*z + 2, 5*y^2 - y*z + 10*x + 2, 5*x*z - x, 5*y*z - y, 10*z - 2]
sage: R.ideal([5,2]).groebner_basis()
[1]

So since singular works for ZZ, I think this patch should also fix it at least for that ring.

Ok, did it now more general. It needed a restructuring of the existing relevant code.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​df26e69

Merge tag '8.7' into t/27445/gb-no-var

[tscrim]

Thank you. I think this is much better and more consistent.

[dkrenn]

Replying to tscrim:

Thank you. I think this is much better and more consistent.

I think so as well. Thank you.